   #copyright

Pythagoras

2007 Schools Wikipedia Selection. Related subjects: Mathematicians

                  Western Philosophy
   Pre-Socratic philosophy
   Pythagoras
         Name:       Pythagoras
        Birth:       ca. 582 BC
        Death:       ca. 507 BC
   School/tradition: Pythagoreanism
    Main interests:  Philosophy of mathematics
    Notable ideas:   Numbers as the ultimate reality
      Influences:    Tasdfasdf
      Influenced:    Plato

   Pythagoras of Samos ( Greek: Πυθαγόρας; circa 582 BC – circa 507 BC)
   was an Ionian ( Greek) mathematician and philosopher, founder of the
   mathematical, mystic, religious, and scientific society called
   Pythagoreans. He is best known for the Pythagorean theorem which bears
   his name. Known as " the father of numbers", Pythagoras made
   influential contributions to philosophy and religious teaching in the
   late 6th century BC. Because legend and obfuscation cloud his work even
   more than with the other pre-Socratics, one can say little with
   confidence about his life and teachings. We do know that Pythagoras and
   his students believed that everything was related to mathematics and,
   through mathematics, everything could be predicted and measured in
   rhythmic patterns or cycles.

   Pythagoras was one of the first to speculate that human life begins
   with a blend of male and female fluids, or semens, originating in body
   parts (Enyclopaedia Britannica). This important idea thus gave forth
   the idea that genetics and heredity required a blend of male and female
   bodies to form new life.

Biography

   Bust of Pythagoras, Vatican
   Enlarge
   Bust of Pythagoras, Vatican
   Pythagoras, the man in the center with the book, in The School of
   Athens by Raphael
   Enlarge
   Pythagoras, the man in the centre with the book, in The School of
   Athens by Raphael

   Pythagoras was born on the island of Samos (Greek East Coast), off the
   coast of Asia Minor. He was born to Pythais (his mother, a native of
   Samos) and Mnesarchus (a merchant from Tyre). As a young man, he left
   his native city for Crotone in Southern Italy, to escape the tyrannical
   government of Polycrates. According to Iamblichus, Thales, impressed
   with his abilities, advised Pythagoras to go to Memphis in Egypt and
   study with the priests there who were renowned for their wisdom. He
   also was discipled in the temples of Tyre and Byblos in Phoenicia. It
   may have been in Egypt where he learned some geometric principles which
   eventually inspired his discovery of the theorem that is now called by
   his name. This possible inspiration is presented as an example problem
   in the Berlin Papyrus.

   Upon his migration from Samos to Crotone, Pythagoras established a
   secret religious society very similar to (and possibly influenced by)
   the earlier Orphic cult.

   Pythagoras undertook a reform of the cultural life of Crotone, urging
   the citizens to follow virtue and form an elite circle of followers
   around himself. Very strict rules of conduct governed this cultural
   centre. He opened his school to male and female students alike. Those
   who joined the inner circle of Pythagoras's society called themselves
   the Mathematikoi. They lived at the school, owned no personal
   possessions and were required to assume a vegetarian diet. Other
   students who lived in neighboring areas were also permitted to attend
   Pythagoras's school. Known as Akousmatics, these students were
   permitted to eat meat and own personal belongings.

   According to Iamblichus, the Pythagoreans followed a structured life of
   religious teaching, common meals, exercise, reading and philosophical
   study. Music featured as an essential organizing factor of this life:
   the disciples would sing hymns to Apollo together regularly; they used
   the lyre to cure illness of the soul or body; poetry recitations
   occurred before and after sleep to aid the memory.

   According to Hermippus of Smytna (De Pythagora, apud: Josephus, Contra
   Apionem, I, 162/165) Pythagoras was familiar and an admirer of Jewish
   customs and wisdom. Hermippus of Smytna says about Pythagoras: "In
   practicing and repeating these percepts he was imitating and
   appropriating the doctrines of Jews and Thracians. In fact, it is
   actually said that that great man introduced many points of Jewish law
   into his philosophy." (trans. H. St. J. Thackeray, The Loeb Classical
   Library, Cambridge (Mass.)-London)

   The history of the Pythagorean theorem that bears his name is complex.
   Whether Pythagoras himself proved this theorem is not known, as it was
   common in the ancient world to credit a famous teacher with the
   discoveries of his students. The earliest known mention of Pythagoras's
   name in connection with the theorem occurred five centuries after his
   death, in the writings of Cicero and Plutarch. It is also believed that
   the Indian mathematician Baudhayana discovered the Pythagorean Theorem
   around 800 BC, about 300 years before Pythagoras.

   Today, Pythagoras is revered as a prophet by the Ahlu l-Tawhīd or Druze
   faith along with his fellow Greek, Plato.

   According to myth, he died at the hands of a soldier, because he
   refused to trample a bean-field while fleeing.

Pythagoreans

   Pythagoras's followers were commonly called "Pythagoreans." For the
   most part we remember them as philosophical mathematicians who had an
   influence on the beginning of axiomatic geometry, which after two
   hundred years of development was written down by Euclid in The
   Elements. The Pythagoreans observed a rule of silence called
   echemythia, the breaking of which was punishable by death. This was
   because the Pythagoreans believed that a man's words were usually
   careless and misrepresented him and that when someone was "in doubt as
   to what he should say, he should always remain silent". Another rule
   that they had was to help a man "in raising a burden, but do not assist
   him in laying it down, for it is a great sin to encourage indolence"
   and they said "departing from your house, turn not back, for the furies
   will be your attendants" this axiom reminded them that it was better to
   learn none of the truth about mathematics, God, and the universe at all
   than to learn a little without learning all. (source The Secret
   Teachings of All Ages Hall, Manly P.). In his biography of Pythagoras
   (written seven centuries after Pythagoras's time) Porphyry stated that
   this silence was "of no ordinary kind." The Pythagoreans were divided
   into an inner circle called the mathematikoi ("mathematicians") and an
   outer circle called the akousmatikoi ("listeners"). Porphyry wrote "the
   mathematikoi learned the more detailed and exactly elaborate version of
   this knowledge, the akousmatikoi (were) those which had heard only the
   summary headings of his (Pythagoras's) writings, without the more exact
   exposition." According to Iamblichus, the akousmatikoi were the
   exoteric disciples who listened to lectures that Pythagoras gave out
   loud from behind a veil. The akousmatikoi were not allowed to see
   Pythagoras and they were not taught the inner secrets of the cult.
   Instead they were taught laws of behaviour and morality in the form of
   cryptic, brief sayings that had hidden meanings. The akousmatikoi
   recognized the mathematikoi as real Pythagoreans, but not vice versa.
   After the murder of Pythagoras and a number of the mathematikoi by the
   cohorts of Cylon, a resentful disciple, the two groups split from each
   other entirely, with Pythagoras's wife Theano and their two daughters
   leading the mathematikoi.

   Theano, daughter of the Orphic initiate Brontinus, was a mathematician
   in her own right. She is credited with having written treatises on
   mathematics, physics, medicine, and child psychology, although nothing
   of her writing survives. Her most important work is said to have been a
   treatise on the principle of the golden mean. In a time when women were
   usually considered property and relegated to the role of housekeeper or
   spouse, Pythagoras allowed women to function on equal terms in his
   society.

   The Pythagorean society is associated with prohibitions, such as not to
   step over a crossbar, and not to eat beans (for the inside of beans
   contain embryos like humans). These rules seem like primitive
   superstition, similar to "walking under a ladder brings bad luck,"
   rules one cannot help but sneeze at. The abusive epithet mystikos logos
   ("mystical speech") was hurled at Pythagoras even in ancient times to
   discredit him. The key here is that "akousmata" means "rules," so that
   the superstitious taboos primarily applied to the akousmatikoi, and
   many of the rules were probably invented after Pythagoras's death and
   independent from the mathematikoi (arguably the real preservers of the
   Pythagorean tradition). The mathematikoi placed greater emphasis on
   inner understanding than did the akousmatikoi, even to the extent of
   dispensing with certain rules and ritual practices. For the
   mathematikoi, being a Pythagorean was a question of innate quality and
   inner understanding.

   Beans, black and white, were the means used in voting. The maxim
   "abstain from beans" was perhaps nothing more than an exhortation to
   not vote. If true, this would be an excellent example of how ideas can
   be distorted when heard second hand and taken out of context. There was
   also another way of dealing with the akousmata — by allegorizing them.
   We have a few examples of this, one being Aristotle's explanations of
   them: "'step not over a balance', i.e. be not covetous; 'poke not the
   fire with a sword', i.e. do not vex with sharp words a man swollen with
   anger, 'eat not heart', i.e. do not vex yourself with grief," etc. We
   have evidence for Pythagoreans allegorizing in this way at least as far
   back as the early fifth century BC. This suggests that the strange
   sayings were riddles for the initiated.

   The Pythagoreans are known for their theory of the transmigration of
   souls, and also for their theory that numbers constitute the true
   nature of things. They performed purification rites and followed and
   developed various rules of living which they believed would enable
   their soul to achieve a higher rank among the gods. Much of their
   mysticism concerning the soul seem inseparable from the Orphic
   tradition. The Orphics advocated various purifactory rites and
   practices as well as incubatory rites of descent into the underworld.
   Pythagoras is also closely linked with Pherecydes of Syros, the man
   ancient commentators tend to credit as the first Greek to teach a
   transmigration of souls. Ancient commentators agree that Pherekydes was
   Pythagoras's most intimate teacher. Pherekydes expounded his teaching
   on the soul in terms of a pentemychos ("five-nooks," or "five hidden
   cavities") — the most likely origin of the Pythagorean use of the
   pentagram, used by them as a symbol of recognition among members and as
   a symbol of inner health (ugieia).

   It was the Pythagoreans who discovered that the relationship between
   musical notes could be expressed in numerical ratios of small whole
   numbers (see Pythagorean tuning). He discovered that by using the ratio
   3/2 one could translate musical notes into mathaematical equations.
   Pythagoras was interested in music and the Pythagoreans were musicians
   as well as mathematicians. He wanted to improve the music of his day,
   which he believed was not harmonious enough and was too chaotic.
   According to legend, the way Pythagoras discovered that musical notes
   could be translated into mathematical equations was when he was walking
   some day and he passed by some blacksmiths, he heard their anvils being
   hit and thought that the sounds they made were beautiful and harmonious
   and decided that whatever scientific law caused this to happen must be
   a mathematical law that could be applied to music. He went to the
   blacksmiths to learn how this had happened by looking at their tools.
   He discovered that it was because the anvils were "simple ratios of
   each other, one was half the size of the first, another was 2/3 the
   size, and so on." The Pythagoreans elaborated on a theory of numbers
   the exact meaning of which is still debated among scholars.

Literary works

   No texts by Pythagoras survive, although forgeries under his name — a
   few of which remain extant — did circulate in antiquity. Critical
   ancient sources like Aristotle and Aristoxenus cast doubt on these
   writings. Ancient Pythagoreans usually quoted their master's doctrines
   with the phrase autos ephe ("he himself said") — emphasizing the
   essentially oral nature of his teaching. Pythagoras appears as a
   character in the last book of Ovid's Metamorphoses , where Ovid has him
   expound upon his philosophical viewpoints.

Influence on Plato

   Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised
   an important influence on the work of Plato. According to R. M. Hare,
   his influence consists of three points: a) the platonic Republic might
   be related to the idea of "a tightly organized community of like-minded
   thinkers", like the one established by Pythagoras in Croton. b) there
   is evidence that Plato possibly took from Pythagoras the idea that
   mathematics and, generally speaking, abstract thinking is a secure
   basis for philosophical thinking as well as "for substantial theses in
   science and morals". c) Plato and Pythagoras shared a "mystical
   approach to the soul and its place in the material world". It is
   probable that both have been influenced by Orphism.

   Plato's harmonics were clearly influenced by the work of Archytas, a
   genuine Pythagorean of the third generation, who made important
   contributions to geometry, reflected in Book VIII of Euclid's Elements.

Influence on Esoteric Groups

   Pythagoras started a secret society called the Pythagorean brotherhood
   devoted to the study of mathematics. This had a great effect on future
   esoteric traditions such as Rosicrucianism and Freemasonry, both of
   which were occult groups dedicated to the study of mathematics, and
   both of which evolved out of the Pythagorean brotherhood. The mystical
   and occult qualities of Pythagorean mathematics are discussed in a
   chapter of Manly P. Hall's The Secret Teachings of All Ages entitled
   Pythagorean Mathematics.

   Pythagorean theory was tremendously influential on later numerology,
   which was extremely popular throughout the Middle East in the ancient
   world. 8th century Islamic alchemist Jabir ibn Hayyan, inventor of
   numerous important chemical processes still in use today, grounded his
   work in an elaborate numerology greatly influenced by Pythagorean
   theory.

Quotes concerning Pythagoras

     * "So greatly was he admired that his disciples used to be called
       'prophets to declare the voice of God'...", Diogenes Laertius,
       Lives of Eminent Philosophers, VIII.14, Pythagoras; Loeb Classical
       Library No. 185, p. 333
     * "...the Metapontines named his house the Temple of Demeter and his
       porch the Museum, so we learn from Favorinus in his Miscellaneous
       History.", Diogenes Laertius, Lives of Eminent Philosophers,
       VIII.15, Pythagoras; Loeb Classical Library No. 185, p. 335
     * "Learn to be silent...Let your quiet mind listen and absorb..."

   Retrieved from " http://en.wikipedia.org/wiki/Pythagoras"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
